Hybrid Rounding Techniques for Knapsack Problems

We address the classical knapsack problem and a variant in which an upper bound is imposed on the number of items that can be selected. We show that appropriate combinations of rounding techniques yield novel and powerful ways of rounding. As an application of these techniques, we present a linear-storage Polynomial Time Approximation Scheme (PTAS) and a Fully Polynomial Time Approximation Scheme (FPTAS) that compute an approximate solution, of any fixed accuracy, in linear time. This linear complexity bound gives a substantial improvement of the best previously known polynomial bounds.Comment: 19 LaTeX page

A special family of Galton-Watson processes with explosions

The linear-fractional Galton-Watson processes is a well known case when many characteristics of a branching process can be computed explicitly. In this paper we extend the two-parameter linear-fractional family to a much richer four-parameter family of reproduction laws. The corresponding Galton-Watson processes also allow for explicit calculations, now with possibility for infinite mean, or even infinite number of offspring. We study the properties of this special family of branching processes, and show, in particular, that in some explosive cases the time to explosion can be approximated by the Gumbel distribution

Clinical and pathomorphological changes in mycotoxicosis of cows

The defeat of feed by microscopic fungi is a fairly common phenomenon at this stage of the management of the agricultural sector. This is due to weather conditions (high rainfall) and errors in harvesting and storage of grain. Feeding affected feed leads to irreversible processes in the body of cows, reducing their productivity. The aim of the study was to establish marker indicators for the rapid diagnosis of mycotoxicoses in cows. So, when exposed simultaneously to T-2 toxin and toxins of the fungus Aspergillus fumigatus, destructive changes in the skin and mucous membranes were diagnosed, and pathology of the limbs was diagnosed, which was characterized by lameness. The laboratory revealed an increase in the level of leukocytes up to 37.1 g/l and a decrease in the content of hemoglobin in the blood of sick animals. Also, a characteristic feature was the latch of the contents of the rumen at pH 8.0, which in turn leads to a decrease in the number of ciliates. Also a sign of poisoning are changes in the fecal matter: liquid, musty odors and with an increased pH of up to 7.5. At the autopsy of the dead animals, a characteristic sign was: necrosis of the mucous membranes of the oral cavity, esophagus, gastrointestinal tract, protein degeneration in the liver and kidneys, and serous pulmonary edema. Infertility is 67.35 %, which leads to multiple unsuccessful insemination, which is due to destructive changes in the organs of the reproductive system. So, in sick animals, ovarian hypotrophy was diagnosed at the level of 54.09 %, ovarian cysts v in 8.18 %, yellow persistent bodies in the postpartum period – 7.54 %. The prospect of further research will be the development of preventive methods for treating cows and increasing their reproductive function of mycotoxicoses

О сведении уравнений Максвелла в волноводах к системе связанных уравнений Гельмгольца

The investigation of the electromagnetic field in a regular homogeneous waveguide reducesto the investigation of two independent boundary value problems for the Helmholtz equation,corresponding to TE- and TM-modes. In the case of an inhomogeneous waveguide TE- andTM-modes are connected to each other, which in numerical experiments can not always be fullytaken into account. In this paper we show how to rewrite the Helmholtz equations in vectorform to express this relationship explicitly.In the article the cylindrical waveguide with perfectly conducting walls is considered, but wedon’t make any assumptions about filling of waveguide. The introduced approach is based ontwo-dimensional analogue of the theorem known in the theory of elastic bodies as the Helmholtzdecomposition. On its basis, we introduce four potentials, instead of two potentials, usuallyused in the theory of hollow waveguides. It is proved that any solution of Maxwell’s equationsin a waveguide that satisfies the boundary conditions of ideal conductivity on the boundariesof a waveguide can be represented with the help of these potentials. The system of Maxwell’sequations is written with respect to these potentials and it is shown that this system has theform of two independent Helmholtz equations in the case of a hollow waveguide.Исследование электромагнитного поля в регулярном волноводе, заполненным однородным веществом, сводится к исследованию двух независимых краевых задач для уравнения Гельмгольца. В случае волновода, заполненного неоднородным веществом, между модами этих двух задач возникает связь, которую в численных экспериментах не всегда удаётся учесть в полной мере. В настоящей статье показано, как переписать уравнения Гельмгольцав векторной форме, чтобы выразить эту связь явно.В работе рассматривается цилиндрический волновод с идеально проводящими стенками,заполнение которого может менять в поперечном сечении произвольным образом. В основе нашего подхода лежит двумерный аналог теоремы, известной в теории упругих тел как декомпозиция Гельмгольца. На её основании будут введены четыре потенциала вместо двух,обычно используемых в теории полых волноводов. Доказано, что любое решение уравнений Максвелла в волноводе, удовлетворяющее краевым условиям идеальной проводимости на стенках волновода, можно представить при помощи этих потенциалов. Система уравнений Максвелла записана относительно этих потенциалов, и показано, что эта система переходит в пару несвязанных уравнений Гельмгольца в случае полого волновода

TECHNOLOGIES OF TISSUE ENGINEERING AND REGENERATIVE MEDICINE

The paper presents the main fundamental and applied results obtained by the Department of Biomedical Technologies and Tissue Engineering over the period of 2010–2014

Single-mode propagation of adiabatic guided modes in smoothly irregular integral optical waveguides

This paper investigates the waveguide propagation of polarized electromagnetic radiation in a thin-film integral optical waveguide. To describe this propagation, the adiabatic approximation of solutions of Maxwell’s equations is used. The construction of a reduced model for adiabatic waveguide modes that retains all the properties of the corresponding approximate solutions of the Maxwell system of equations was carried out by the author in a previous publication in DCM & ACS, 2020, No 3. In this work, for a special case when the geometry of the waveguide and the electromagnetic field are invariant in the transverse direction. In this case, there are separate nontrivial TEand TM-polarized solutions of this reduced model. The paper describes the parametrically dependent on longitudinal coordinates solutions of problems for eigenvalues and eigenfunctions - adiabatic waveguide TE and TM polarizations. In this work, we present a statement of the problem of finding solutions to the model of adiabatic waveguide modes that describe the stationary propagation of electromagnetic radiation. The paper presents solutions for the single-mode propagation of TE and TM polarized adiabatic waveguide waves.В работе представлено исследование волноводного распространения поляризованного электромагнитного излучения в тонкоплёночном интегральнооптическом волноводе. Для описания этого распространения используется адиабатическое приближение решений уравнений Максвелла. Построение редуцированной модели для адиабатических волноводных мод, сохраняющей все свойства соответствующих приближённых решений системы уравнений Максвелла, было проведено автором в предыдущей публикации в DCM&ACS, 2020, № 3. В настоящей работе исследование проведено для частного случая, когда геометрия волновода и электромагнитное поле инвариантны в поперечном направлении. В этих условиях существуют раздельные нетривиальные ТЕи ТМ-поляризованные решения указанной редуцированной модели. В работе описываются параметрически зависящие от продольных координат решения задач на собственные значения и собственные функции - адиабатические волноводные ТЕи ТМ-поляризации. В работе приводится постановка задачи отыскания решений модели адиабатических волноводных мод, описывающих стационарное распространение электромагнитного излучения. Представлены решения для одномодового распространения ТЕи ТМ-поляризованных адиабатических волноводных волн